Find the differential of the function w = x sin (4yz4). = dx +dy + Note: Your answers should be expressions of x, y and z; e.g. "3xy + 4z" dw = dz

Q: 2+ 4 y=x-2 f(x) -X

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Q: Evaluate the integral I. I 1 = f (e¹i + 3t²j + ln (5t) k) dt i + j+ k + C

A: The given integral

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A: The given differential equation iswhere,Show that the solution to the differential equation is

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Q: Find the indefinite integral on the domain of positive real numbers for the following function: 3…

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A: Answer V = 76.595 unit ³Explanation: Thank you ?

Q: 20. Given a = [3, -5,1], b = [-2,4,-1] and 2 = [7,3, -2], find a) b.č b) axč c) , the angle between…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub parts…

Q: 12. Convert to polar form x² + 4x +y² +4y=0

A: we need to convert into the polar form.

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Q: use the definition of a derivative to find f'(x): 1) f(x) = sqrt(x-6) 2) f(x) = 1+1/x

A: The objective of this question is to find the derivative of the given functions using the definition…

Q: α. Σ=of (2k) b.Σ=2f()_c.Σ=19(f(k)).

A: we need to evaluate the sum."Note that as per the rules, we are supposed to answer the first three…

Q: (b) Show that 0 sin(x) cos(nx)dx 1+(-1)" 1-n²

A: To show that, .

Q: Suppose that f(1) = 2, f(4) = 6, f'(1) = 6, f'(4) = 5, and f" is continuous. Find the value of 4…

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Q: 2. Consider the sequence 2,2 + √2,2 + √√2+√√2,2+√√2+√√2+ √2,.... Assuming that the sequence…

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Q: where a, b € Z, b‡ 0. 3. Recall that a rational number r EQ is a number of the form r Decide whether…

A: The objective of the question is to determine the validity of two claims about rational numbers and…

Q: 2. (a) (b) Consider f(x) = 10 (x − 1)(x² + 9) Decompose f(x) = = dx. 10 (x − 1)(x² +9) more space,…

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Q: 3) What does the matrix 1 0 0 0 1 0 001 represent?

A: The matrix represents the identity matrix of size 3x3.Explanation:In the given, the matrix…

Q: Find if the series converges or diverges.

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A: Given that point  is on the graph

Q: Find if the series converges or diverges.

A: Series is convergent.Explanation: For any query with solution please ask in the comment box.

Q: (f) / 1 x(lnx)³ dx

A: Answer No. (f): To evaluate the following integral.Note: Since you have posted multiple questions…

Q: r₁ (t) = (lt, 1, -1²), r₂(t) = (-1, e¹, −8) (r₁(t) · r₂(t)) = dt

A: Product rule

Q: Consider regular pentagons with side length  s , area  a , and perimeter  p . Suppose  f ,  g ,  h ,…

A: The objective of the question is to find the area of a regular pentagon whose perimeter is 148 cm…

Q: The graph of a periodic function f is shown below. 4 √3 2 1 -1 f(0) 1.57 3.14 4.71 6.28

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Q: A graph is given. Tell where f(x) is concave up, where it is concave down, and where it has points…

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Q: (b) (x²+xy) = y² y = 1 when x = 2 Substitution

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Q: Sketch a single graph of a function with all of the following properties: i. f(1)=2, III. lim…

A: We solve given problem using the concept of limits.

Q: Determine the convergence or divergence of the series.

A: The answer is given below.Explanation:

Q: a) Make a sketch of: f(x)= x², if x 2 Clearly label each part on your graph. You must use graph…

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Q: A company's total sales (in millions of dollars) + months from now are given by S(t) = 0.03t³ +0.5t²…

A: Given: To Find: To determine the units of  .

Q: 3. Let f(x)= x+ - 8x2. What are the critical number(s)? a. X = = 0, x=-4, and x = 4 b. x = -2 and x…

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Q: With U.S. Department of Health and Human Services data from 2002 and projected to 2024, the total…

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Q: Use f-¹(f(x)) = x to determine a. Iff-¹(x) = - b. Evaluate f-¹ (8) is the inverse function of f(x) =…

A: We need to use the given property to solve the question.

Q: Perform long division on the integrand, write the proper fraction as a sur of partial fractions, and…

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Q: The amount of medicine m in the blood during a four-hour treatment is given as me²t = 3t. Determine…

A: The amount of medicine m in the blood during a four hour treatment is given as

Q: State the form of the partial fractions decomposition for the following anti-derivatives: X-1…

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Q: Find if the series converges or diverges.

A: The answer is given below.Explanation:

Q: The angle below has a measure of 5.2 radians. • X= Determine the exact coordinates of the terminal…

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Q: Consider the function f(0) = 4 sin(20) where represents a number of radians. a. Complete the…

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Q: Prove the following statement: If two vectors a and b are parallel, then a×b=0. (Express…

A: To prove If two vectors a and b are parallel, then

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the…

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